1. [9 pts] Solve the following initial value problem. ť · y'(t) +ť.y(t) = y2, y(1)...
6. (2 pts) Consider the following initial value problem: y' = (t + y)?y2 + sin(yº) + yety, y(0) = 0. This initial value problem satisfies the existence and uniqueness theorem criteria using interval (-0, 0) for both thet and y variables, and hence has a unique solutoin. Find this unique solution. Hint: None of the techniques we've learned for explicitly solving will work. Instead, try plugging the initial condition into the differential equation and think about what that tells...
22 - y2 (1 point) Solve the initial value problem y' = · with y(2) = 2 xy help (equations)
3) Solve the following initial value problem. ( 1; 0 <t y" + y = f(t), y(0) = 2, y'(0) = -1, where f(t) = } nere -1; En VI t
Alpha=9 beta=3 yazarsin 1. Consider the following initial-value problem. y' = e(1+B)t ln(1 + y2), 0<t<1 y (0) = a +1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t = 0.5. {"
5. (13 pts) Solve the following initial value problem: y" + 2y' + y-ul (t)o V"(0) 0. y(0) 0, (t-1), -(t1) cos
1. Consider the following initial-value problem. s y' = e(1+B)t In(1 + y2), 0<t<1 y (0) = a +1 a) b) t=0.5. Determine the existence and uniqueness of the solution. Use Euler's method with h = 0.25 to approximate the solution at
Find y(t) solution of the initial value problem 2 y2 +bt2 y'= y(1) = 1, t>0, ty
4. [15 pts.] For 2y' = -tan(t)(y2 – 1) (a) find the general solution (solve for y(t)); (b) solve an initial value problem y(0) = -1/3 (state the domain of definition of the solution).
(1 point) Solve the initial value problem 2yy' + 4 = y2 + 4.r with y(O) = 5. a. To solve this, we should use the substitution help (formulas) With this substitution, y = help (formulas) y' = help (formulas) Enter derivatives using prime notation (e.g., you would enter y' for ). b. After the substitution from the previous part, we obtain the following linear differential equation in 2, u, u'. help (equations) C. The solution to the original initial...
I. Use Euler's method with step size h = 0.1 to numerically solve the initial value problem y,--2ty+y2, y(0) 1 on the interval 0 < t 2. Compare your approximations with the exact solution. I. Use Euler's method with step size h = 0.1 to numerically solve the initial value problem y,--2ty+y2, y(0) 1 on the interval 0